Answer:
h = x + 1.5
Step-by-step explanation:
Start with the width. The width = x
The length is 5 times the width = 5*x or 5x
The volume of this is
Two things V = 5x^3 + 7.5x^2V = l * w * h Substitute the length and width into the raw formula5x^3 + 7.5x^2 = 5x * x * h
5x^3 + 7.5x^2 = 5x^2 * h Divide both sides by 5x^2
5x^3 / 5x^2 + 7.5x^2 / 5x^2 = 5x^2*h/ 5x^2
x + 1.5 = h <<<< Answer
The line segment is dilated by a factor of 1/2 with respect to the origin. What is the length of the dilated line segment?
A. 1 unit
B. 2 units
C. 3 units
D. 4 units
The length of the dilated line segment is 2 units. ( option B)
A scale factor is a ratio that describes the proportional change in size between two similar geometric figures.
Scale factor = Dimension of new length /dimension of original length
The dimension of the original length is 4 units
scale factor = 1/2
let the new length be x
Therefore;
1/2 = x/4
2x = 4
x = 4/2 = 2units
Therefore, the length of the dilated segment is 2units
The following is an incomplete paragraph proving that the opposite angles of parallelogram ABCD are congruent: According to the given information, and . Using a straightedge, extend segment AB and place point P above point B. By the same reasoning, extend segment AD and place point T to the left of point A. Angles BCD and PBC are congruent by the Alternate Interior Angles Theorem. Angles PBC and BAD are congruent by the ____________. By the Transitive Property of Equality, angles BCD and BAD are congruent. Angles ABC and BAT are congruent by the _____________. Angles BAT and CDA are congruent by the Corresponding Angles Theorem. By the Transitive Property of Equality, ∠ABC is congruent to ∠CDA. Consequently, opposite angles of parallelogram ABCD are congruent. What theorems accurately complete the proof?
Given a parallelogram ABCD, refer to the attached image.
To prove: Opposite angles are congruent.
Proof:
According to the given information,
Step 1: Using a straightedge, extend segment AB and place point P above point B.
Step 2: By the same reasoning, extend segment AD and place point T to the left of point A.
Step 3: Angles BCD and PBC are congruent by the Alternate Interior Angles Theorem.
Step 4: Angles PBC and BAD are congruent by the Corresponding Angles Theorem. ( If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent. Corresponding angles are the angles which occupy the same relative position at each intersection where a straight line crosses two others.)
Step 5: By the Transitive Property of Equality, angles BCD and BAD are congruent.
Step 6: Angles ABC and BAT are congruent by the Alternate Interior Theorem.(The Alternate Interior Angles theorem states, if two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent. Alternate Interior angles are a pair of angles on the inner side of each of those two lines but on opposite sides of the transversal.)
Step 7: Angles BAT and CDA are congruent by the Corresponding Angles Theorem.
Step 8: By the Transitive Property of Equality, ∠ABC is congruent to ∠CDA. Consequently, opposite angles of parallelogram ABCD are congruent.
The proof requires the use of specific theorems such as the Vertical Angles Theorem and Corresponding Angles Theorem to establish the congruence of angles in a parallelogram.
Theorems that accurately complete the proof:
Angles PBC and BAD are congruent by the Vertical Angles Theorem.
Angles ABC and BAT are congruent by the Corresponding Angles Theorem.
Theorem 12 states that if two angles are congruent, their supplementary angles are also congruent.
Which of the following is a logarithmic function? A. Y=0.25X B. Y=x^0.25 c.y=log25^x d.y=(0.25)^x
Answer:
The correct option is C .
Step-by-step explanation:
A logarithm function is written in the form of [tex]y=log_ax[/tex],
Since, y = 0.25x is the type of function y = mx + c,
Which is the general form of a linear function,
⇒ y = 0.25x is not a logarithm function,
[tex]y=x^{0.25}[/tex] is the type of function [tex]y=kx^a[/tex], where k and a are any real number,
Which is the general form of a power function,
⇒ [tex]y=x^{0.25}[/tex] is not a logarithmic function.
[tex]y=(0.25)^x[/tex] is the type of function [tex]y=ab^x[/tex]
Which is the general form of exponential function,
⇒ [tex]y=(0.25)^x[/tex] is not a logarithmic function,
Hence, only the function in option C has written in the form of [tex]y=log_ax[/tex].
Option C is correct.
Can someone help me please!!!
PLEASE HELP
Is this A, B, or C?
In a Quadratic Regression problem, a graph is a perfect fit for the data when r = ? a. 1 c. 2 b. 0 d. 100 Please select the best answer from the choices provided A B C D
Answer:
the answer is A on edge :)
Step-by-step explanation:
The graph that is a perfect fit for the given data in a quadratic regression problem is when r is; A: 1
What is a quadratic regression?Quadratic regression is defined as a statistical technique that is used to find the equation of the parabola that best fits a set of data.
Now, this type of regression is an extension of simple linear regression that is used to find the equation of the straight line that best fits a set of data.
Thus, in this type of regression, we say a graph is a perfect fit when r = 1.
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The formula used to find the length of a line segment in space.
if youre doing the vocab thing -- Distance
if the remainder on division of x^3+2x^2+kx+3 by x-3 is 21,find the quotient and the value of k. Hence,find the zeroes of the cubic polynomial x^3+2x^2+kx-18.
You are looking for your first credit card. You plan to use this credit card only for emergencies and to pay the credit card balance in full each month. Which credit card feature is most important?
a.
No annual fee
b.
Low APR
c.
Generous rewards program
d.
No balance transfer fee
Answer:
A
Step-by-step explanation:
EDU
The credit card feature of "No annual fee" represents the correct alternative of the given ones.
What is credit card?A credit card is a payment card issued to users to enable the cardholder to pay a merchant for goods and services based on the cardholder's accrued debt.
Given is that you are looking for your first credit card. You plan to use this credit card only for emergencies and to pay the credit card balance in full each month.
The credit card feature of "No annual fee" is suitable for emergencies.
Therefore, the credit card feature of "No annual fee" represents the correct alternative of the given ones.
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Determine the number of possible triangles, ABC that can be formed given angle A=30 degrees, a=4 and b=6
Answer:
One possible triangle
Step-by-step explanation:
Given that in a triangleABC given one angle A =30 , two sides a and b
We can use sine angle formula for triangles
[tex]\frac{a}{sinA} =\frac{b}{sinB} =\frac{c}{sinC}[/tex]
Substitute to get
[tex]\frac{4}{sin30} =\frac{6}{sin B} =\frac{c}{sinC}[/tex]
[tex]sin B = 0.75\\B=48.6[/tex]
C=[tex]180-30-48.6\\= 101.4[/tex]
[tex]c=8sin 101.4\\c=7.842[/tex]
There can be only one triangle
in quadrilateral abcd , angle A=57 degrees , angle B=65 degrees and angle c=118 degrees What is the measure of an exterior angle at D
What is the sum of 4.9 × 102 and 6.8 × 103?
( one answer )
Answer:the answer is 7290
Step-by-step explanation:
From the given expression
4.9*10^2 =4.9*100=490
and
6.8*10^3=6.8*1000=6800
490+6800=7290
Which is the ratio for sin a written as a fraction in simplest form
your Answer issss:
√3/2
Would be glad if you answer my question!
Tickets for the school play cost $17 each. Gary wrote the expression n X 17 to find the cost of n tickets to the play. He used the Distributive Property to find the product. Use the Distributive Property to write Gary's expression another way.
Michelle draws a card from a standard deck of 52 cards. She replaces the card and draws a second card. What is the probability that she draws a red card and then a black card
A) 1/16
B)1/26
C)1/4
D)1/52
reflect point A(5, 7, 2) across the xz-plane. where will the new point be located?
(-5, -7, 2)
(-5, -7, -2)
(-5, 7, -2)
(5, -7, 2)
The city of Beijing has a population of more than 10 to the 7th power people. Write 10 to the 7th power without using an exponent
Answer:
[tex]10\times 10\times 10\times 10\times 10\times 10 \times 10[/tex]
Step-by-step explanation:
Exponentiation is the operation used to write the product of two or more equal factors. This expression can written as follows:
[tex]a^n\\\\Where:\\\\a=Base\\n=Exponent[/tex]
That is, [tex]a^n[/tex] is the product of multiplying n bases:
[tex]a^n=a\times...\times...\times a[/tex]
In this sense:
[tex]10^7=10\times 10\times 10\times 10\times 10\times 10 \times 10[/tex]
At a furniture manufacturer, worker A can assemble a shelving unit in 5 hours. Worker B can assemble the same shelving unit in 3 hours. Which equation can be used to find t, the time it takes for worker A and worker B to assemble a shelving unit together?
The equation 1/t = 1/5 + 1/3 can be used to find the time it takes for worker A and worker B to assemble a shelving unit together.
To find the time t it takes for worker A and worker B to assemble a shelving unit together, we need to add their work rates.
Worker A's work rate is 1 unit per 5 hours (or 1/5 units per hour), and worker B's work rate is 1 unit per 3 hours (or 1/3 units per hour).
The combined work rate is the sum of their individual work rates:
1/5 + 1/3 = (3 + 5) / 15 = 8 / 15 units per hour
If t is the time they take together to complete one shelving unit, then their combined work rate is 1 unit per t hours. Setting this equal to their combined rate, we get:
1/t = 8/15
Solving for t gives:
t = 15/8 hours
Therefore, the equation 1/t = 1/5 + 1/3 can be used to find the time it takes for worker A and worker B to assemble a shelving unit together.
in a given circuit, the supplied voltage is 1.5 volts, and the resistor value is 3 ohms. use ohm's law to determine the current in the circuit
Final answer:
The current in a circuit with a supplied voltage of 1.5 volts and a resistance of 3 ohms is calculated using Ohm's Law (I = V/R), resulting in a current of 0.5 amperes.
Explanation:
Using Ohm's Law to Calculate Current
To determine the current in a circuit with a supplied voltage of 1.5 volts and a resistor value of 3 ohms, we can use Ohm's Law, which is stated as I = V/R, where I is the current, V is the voltage, and R is the resistance. Plugging in the values, we have I = 1.5 volts / 3 ohms. Therefore, I = 0.5 amperes or 500 milliamperes. This is the current flowing through the circuit.
Ohm's Law is a fundamental principle in physics used for analyzing simple circuits where the relationship between voltage, current, and resistance is linear. Remember that this law holds true for ohmic materials where the resistance remains constant over a range of voltages and temperatures.
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Danielle poured 3/4 gallon of water from a 7/8 gallon bucket. How much water is left in the bucket?
Maria sets a goal of jogging 17.5miles this week. She plans on running 2.75 miles each day for 7 days . If she follows her plan which is true
If a 10. m3 volume of air (acting as an ideal gas) is at a pressure of 760 mm and a temperature of 27 degrees Celsius is taken to a high altitude where the pressure is 400. mm Hg and a temperature of -23 degrees Celsius, what volume will it occupy? (Hint: remember the temperature must be in Kelvin)
Answer:
16. m3
Step-by-step explanation:
27 degrees Celsius= 27+273= 300 kelvin
23 degrees Celsius= -23+273=250 kelvin
Combined Gas Law: P1V1/T1 = P2V2/T2
(760mm*10 m3)/300 K=(400mm*x m3)/250 K x= 16. m3
The volume that it will occupy is 16. m3.
(Don't forget the sig fig, 15.83--->16. because the question said 10.)
A group of college students are volunteering for Help the Homeless during their spring break. They are putting the finishing touches on a house they built. Working alone, Irina can paint a certain room in 9 hours. Paulo can paint the same room in 8 hours. Write an equation that can be used to find how long it will take them working together to paint the room. How many hours will it take them to paint the room? If necessary, round your answer to the nearest hundredth
The combined work rate can be found by using the equation for combined rate.
The correct responses;The time it will take them working together is; [tex]\displaystyle \underline{\frac{1}{t_b} = \frac{1}{t_1} + \frac{1}{t_2} }[/tex]The number of hours it will take them working together to paint the room is approximately 4.24 hours. The method by which the above responses are obtained:The time it takes Irina to paint the room alone, t₁ = 9 hours
Time it takes Paulo to paint the room, t₂ = 8 hours
Required:
To write the equation for the combined rate of Irina and Paulo
Solution:The equation that gives the time, [tex]\mathbf{t_b}[/tex], it will take both Irina and Paulo to paint the room together is given by the combined rate formula, as follows;
[tex]\displaystyle \underline{ \frac{1}{t_b} = \frac{1}{t_1} + \frac{1}{t_2}}[/tex]Required:The duration it will take them to paint the room when working together.
Solution:The time it will take them to paint the room together is found as follows;
[tex]\displaystyle \frac{1}{t_b} = \mathbf{\frac{1}{9} + \frac{1}{8}}[/tex]
Which gives;
[tex]\displaystyle \frac{1}{t_b} = \frac{8 + 9}{9 \times 8} = \mathbf{\frac{17}{72}}[/tex]
Therefore;
[tex]\displaystyle t_b = \frac{72}{17} \approx \mathbf{4.24}[/tex]
The time it takes Irina and Paulo to paint together, [tex]t_b[/tex] ≈ 4.24 hrs.Learn more about combined rate of work here:
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Which list shows all the factors of 18?
1, 2, 3, 4, 6, 9, 18
1, 2, 3, 6, 9, 18
2, 3, 4, 6, 9
2, 3, 6, 9
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Which graph represents the function over the interval [−3, 3]?
Third graphrepresents the function [tex]f\left( x \right) = \left\lfloor x \right\rfloor-2[/tex] over the interval [tex]\left[ { - 3,3} \right].[/tex]
Further explanation:
Given:
The function is [tex]f\left( x \right) = \left\lfloor x \right\rfloor- 2.[/tex]
The function is defined in the interval [tex]\left[ {-3,3}\right].[/tex]
Explanation:
The greatest integer function is represented [tex]y = \left\lfloor x \right\rfloor.[/tex]
The greatest integer can also be known as floor function. The function is integral part of real numbers.
The values of greatest function [tex]f\left( x \right)= \left\lfloorx \right\rfloor- 2[/tex] in interval [tex]\left[{ - 3,3}\right][/tex] can be obtained as follows,
Substitute [tex]-3[/tex] for [tex]x[/tex] in the function [tex]f\left( x \right)= \left\lfloor x \right\rfloor- 2.[/tex]
[tex]\begin{aligned}f\left({- 3} \right)&=\left\lfloor{ - 3} \right\rfloor- 2\\&=- 3- 2\\&=- 5\\\end{aligned}[/tex]
Substitute [tex]3[/tex] for [tex]x[/tex] in the function [tex]f\left( x \right)=\left\lfloor x \right\rfloor- 2.[/tex]
[tex]\begin{aligned}f\left( 3 \right)&= \left\lfloor3\right\rfloor- 2\\&=3- 2\\&=1\\\end{aligned}[/tex]
The minimum value of the function in [tex]\left[ { - 3,3} \right] {\text{is}\: \boxed{ - 5}.[/tex]
The maximum value of the function in [tex]\left[ { - 3,3} \right] {\text{is}\: \boxed{1}.[/tex]
Third graphrepresents the function [tex]f\left( x \right)=\left\lfloor x\right\rfloor- 2[/tex] over the interval [tex]\left[{ - 3,3}\right].[/tex]
Kindly refer to the image attached.
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Answer details:
Grade: High school
Subject: Mathematics
Chapter: Number system
Keywords: factor, factorization, polynomial, quadratic, cubic, greatest common factor, groups, multiplication, product, identities, common factor, expression, terms, grouping.
Instructions:Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.
is parallel to . and are perpendicular to and .
The ratio of the lengths of and is
:
.
Answer:
The ratio of the lengths of PR and QS is 1 : 1
Step-by-step explanation:
If your question is based on this exercise:
PQ Is parallel to RS. PR and QS are perpendicular to PQ and RS
Here is why
A rectangle is 2 times as long as it is wide. if the area is 18 square feet, find its perimeter.